Multi Spoke Beamforming For Low Power Wide Area Satellite and Terrestrial Networks

ABSTRACT

Wireless communication method and apparatus to enable communications between a plurality of endpoints and a satellite or terrestrial gateway integrated with a plurality of oblong shaped antenna arrays. The wireless communication method leverages data symbols that are orthogonally modulated. The method permits the use of a plurality of compact oblong shaped antenna arrays to increase network capacity and reduce endpoint power consumption.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.17/391,914 filed on Aug. 2, 2021, the disclosure of which isincorporated herein by reference.

FIELD OF THE INVENTION

The present application relates to apparatuses and methods to enablehigh capacity satellite and terrestrial low power wide area networks forconnecting Internet of Things (IoT) devices to the internet.

BACKGROUND

Low power wide area networks (LPWAN) are used to connect battery poweredsensors and other Internet of Things (IoT) devices, that are referred toherein collectively as “endpoints”, to the internet over long distances.As the demand for LPWAN connectivity services grows, there is a growingneed for (1) connectivity that is low cost and reliable at a globalscale and (2) a network that can scale to Billions of IoT endpoints. Lowcost connectivity at a global scale is challenging due to the cost ofinstalling terrestrial gateways across the vast area required to coverthe world's land mass. Furthermore, providing connectivity over oceansis not possible with terrestrial gateways. Scaling to Billions of IoTdevices at a low cost is also challenging due to the high cost oflicensed spectrum and the limited amount of unlicensed spectrumavailable.

One approach to reduce the cost of building a LPWAN and improving thewireless network capacity is to leverage the spatial domain by usingmultiple antennas at the gateway, where the antennas operate together totransmit or receive a given signal, this is called beamforming. Wirelessreceive beamforming leverages a plurality of antennas to collect radioenergy from one or more specific directions. Wireless transmitbeamforming leverages a plurality of antennas to focus radio energytowards one or more specific directions. Beamforming antenna arrays aretypically arranged as either one dimensional antenna arrays calledlinear arrays or two dimensional antenna arrays. A two dimensionalantenna array is typically arranged as a square antenna array but canalso be oblong shaped. A linear antenna array is able to focus thewireless energy along only one dimension (the dimension along the lineformed by the antenna array). A square antenna array is able to focusthe wireless energy along both dimensions of the array. The radio beamthat is formed along a specific dimension of the antenna array has abeam width that is proportional to the size of the antenna array alongthe respective dimension.

Wireless beamforming technology enables radios to use the spatial domainin addition to the time and frequency domains to improve range,reliability and capacity. Single antenna radios are limited toleveraging time and frequency resources within the geographic region inwhich the antenna points towards. Constructing large antenna arraystypically requires a large volume, making it difficult to integrate intosmall satellites.

Satellites integrated with radio gateways can serve as a global lowpower wide area network platform for connecting sensors and other IoTendpoints to the internet. Because satellites typically have an altitudeof around 500 Km or greater, significant coverage is provided even witha single satellite. The downside of having significant coverage is thata radio gateway mounted on a satellite needs to handle a higher level ofuplink and downlink traffic than terrestrial gateways need to handle dueto the larger geographic areas covered by the satellite. The secondchallenge with satellites are the high launch costs, where the coststypically increase linearly with the volume of the satellite. It is thuspreferred to design a satellite to be as small as possible to minimizecost while at the same time providing adequate network capacity tohandle a large number of endpoint traffic. This disclosure discussesapparatuses and methods that leverages a plurality of oblong shapedantenna arrays to minimize satellite volume while maximizing wirelessnetwork capacity for satellite based gateways and also discusses theapplicability to terrestrial based gateways.

BRIEF SUMMARY OF THE INVENTION

Offered is an apparatus for building satellite based wirelesscommunication gateways. The apparatus comprises of a plurality of oblongshaped antenna arrays that are not parallel to each other, each antennaarray comprising of foldable modules that fold into the satellitehousing. Each module comprising radio beamforming circuitry and solarcells to enable small volume satellites with high network capacity.

Offered is a method to decode orthogonally modulated symbols from aplurality of oblong shaped antenna arrays, where the antenna arrays aremounted either on a satellite, aircraft or earth based structures. Themethod allows for higher network capacity and lower endpoint energyconsumption compared to a gateway that uses a single square antennaarray of equivalent volume.

Offered is a method to correct for Doppler shifts of endpoint radiotransmissions arriving at a moving satellite that includes a pluralityof oblong shaped antenna arrays.

Offered is a method to estimate the position and attitude of a satellitethat is mounted with a plurality of oblong shaped antenna arrays. Themethod leverages ground based transmitters with known positions. Themethod can complement or replace other satellite position and attitudeestimation methods such as using magnetic sensors and star trackers forattitude estimation and using the Global Positioning System (GPS) forposition estimation.

Additional features and advantages of the disclosure will be describedbelow. It should be appreciated by those skilled in the art that thisdisclosure may be readily utilized as a basis for modifying or designingother structures for carrying out the same purposes of the presentdisclosure. It should also be realized by those skilled in the art thatsuch equivalent constructions do not depart from the teachings of thedisclosure as set forth in the appended claims. The novel features,which are believed to be characteristic of the disclosure, both as toits organization and method of operation, together with further objectsand advantages, will be better understood from the following descriptionwhen considered in connection with the accompanying figures. It is to beexpressly understood, however, that each of the figures is provided forthe purpose of illustration and description only and is not intended asa definition of the limits of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the presentinvention will become more apparent from the subsequent descriptionthereof, presented in conjunction with the following drawings, wherein:

FIG. 1 is a top view of a satellite integrated with two linear antennaarrays.

FIG. 2 is a top view of a satellite integrated with four linear antennaarrays.

FIG. 3A is a bottom view of a satellite integrated with two linearantenna arrays.

FIG. 3B is a bottom view of a satellite integrated with two rectangularantenna arrays.

FIG. 4 is a bottom view of a satellite integrated with four linearantenna arrays.

FIG. 5 is a side view of a linear antenna array that is partiallyfolded.

FIG. 6 is a side view of a linear antenna array that is fully folded.

FIG. 7 illustrates multiple antenna modules interconnected with eachother.

FIG. 8 is a top and bottom view of an antenna module.

FIG. 9 is a side view of a satellite with two linear antenna arrays.

FIG. 10 is a side view of a satellite with four linear antenna arrays.

FIG. 11 is a side view of a satellite with linear antenna arrays foldedinside.

FIG. 12 is a top view of a satellite with two linear antenna arraysfolded inside.

FIG. 13A is a block diagram of an antenna module receiver electronics.

FIG. 13B is a block diagram of an antenna module transmitterelectronics.

FIG. 14 depicts multiple receive radio beams being generated by a linearantenna array with N antenna elements.

FIG. 15 illustrates the orbital frame of reference.

FIG. 16 illustrates a contour plot of the radio beam energy for a twospoke linear antenna array.

FIG. 17 illustrates the column beams generated by the x antenna spoke.

FIG. 18 illustrates the row beams generated by the y antenna spoke.

FIG. 19 illustrates a matrix of row and column beams generated by a twospoke linear antenna configuration.

FIG. 20 depicts a Fourier Transform of an M-ARY FSK symbol with M=256.

FIG. 21 depicts a Spectrogram of two M-ARY FSK symbols that overlap intime but not frequency.

FIG. 22 depicts symbols from two endpoints being transmittedsimultaneously and the symbols received by the same column antenna beambut different row antenna beams.

FIG. 23 depicts a decoding ambiguity case.

FIG. 24 illustrates a flowchart for decoding M-ARY orthogonal signalsusing multiple oblong shaped antenna arrays.

FIG. 25 illustrates a block diagram of an M-ARY FSK multi spoke signaldecoder.

FIG. 26 illustrates a block diagram of a Chirp Spread Spectrum multispoke signal decoder.

FIG. 27A illustrates sets of Direct Sequence Spread Spectrum signalsthat are orthogonal in the code domain.

FIG. 27B illustrates time shifts of a Direct Sequence Spread Spectrumsignal that is self orthogonal.

FIG. 28 illustrates a block diagram of a Direct Sequence Spread Spectrummulti spoke signal decoder where the incoming signal is a selforthogonal signal.

FIG. 29 illustrates a block diagram of a Direct Sequence Spread Spectrummulti spoke signal decoder where the signal set is orthogonal in thecode dimension.

FIG. 30A illustrates orthogonally modulated symbols over the frequencydimension.

FIG. 30B illustrates orthogonally modulated symbols over the frequencyand time dimensions.

FIG. 30C illustrates orthogonally modulated symbols over the frequency,time and code dimensions.

FIG. 31 is a plot of the Doppler shift of the radio carrier wave of areceived endpoint packet as observed by a Low Earth orbiting satellite.

FIG. 32 is a plot of the change in Doppler shift of the carrier wave ofa received endpoint packet as observed by a Low Earth orbiting satelliteover a 50 mS preamble duration.

FIG. 33 depicts a block diagram of an M-ARY orthogonal signal decoderwith Doppler frequency correction functionality.

FIG. 34 depicts an architecture for satellite attitude estimation usingground based transmitters with known positions.

FIG. 35 depicts a terrestrial wireless network deploying two spatiallyseparated linear antenna arrays.

FIG. 36 depicts the radio beams formed by a terrestrial wireless networkdeploying two spatially separated linear antenna arrays.

FIG. 37 depicts an endpoint automatically switching between a BluetoothLow Energy or WiFi network and a terrestrial LPWAN and a satellite LPWANusing the same radio.

FIG. 38 depicts a satellite with two antenna arrays transmitting acolumn beam and a row beam that is scanned along the ground and isreceived by an endpoint, the endpoint using these signals to estimateits positioning.

FIG. 39A depicts a satellite flying over the United States of Americawith two urban areas contained within a beam formed by the x antennaspoke.

FIG. 39B depicts a satellite flying over the United States of Americawith one urban area contained within a beam formed by the x antennaspoke.

DETAILED DESCRIPTION

This disclosure is directed to wireless communication methods thatenhance the performance of radio systems that leverage a plurality ofoblong shaped antenna arrays. In the disclosure, an oblong shapedantenna array is also referred to as an antenna spoke. FIG. 1illustrates a top view of a satellite which includes two linear antennaspokes 1. The embodiment in FIG. 1 includes solar cells 2 mounted on thetop of the antenna array for powering the satellite electronics. Eachantenna spoke has two branches that can optionally be offset in space asshown in the figure to allow for more flexibility when mounting inside asatellite housing. FIG. 2 illustrates a satellite with 4 antenna spokes.Alternate embodiments can include any plurality of antenna spokes. Theantennas for each spoke are mounted so that the array of antennas arenadir facing (point towards the earth). FIG. 3A illustrates a bottomview of a two spoke linear antenna array mounted on a satellite withantennas 3 mounted along the spokes. FIG. 3B illustrates a bottom viewof a two spoke rectangular antenna array where each spoke is twoantennas wide. In an embodiment, antenna elements are spaced by around ½of a wavelength of the radio carrier wave, alternate embodiments canhave antenna spacing with smaller or larger spacing. Larger antennaspacing provides increased spatial resolution but increases the volumeof the antenna array. FIG. 3A and FIG. 3B illustrate antenna arrays thatuse helical antenna elements, but other types of antenna elements thatcan be used include but are not limited to a monopole antenna, dipoleantenna, or an aperture fed or probe fed patch antenna. FIG. 4illustrates the bottom view for a 4 spoke linear antenna array. Theantenna spokes consist of one or more foldable modules where each modulecontains one or more antennas. Each antenna spoke is stowed away insidethe satellite housing in a folded configuration before the satellite isdeployed. FIG. 5 illustrates an embodiment of the antenna spoke whichcontains two antennas 6 per module in a partially folded configurationand FIG. 6 illustrates the spoke in a fully folded configuration. Theantenna modules are interconnected both mechanically and electrically 5along the edges of the circuit boards 4. One of the electrical wiresdistributes a common Radio Frequency (RF) local oscillator signal from aseparate module inside the satellite housing to all of the antennamodules. In an alternate embodiment, the RF local oscillator isdistributed from one of the modules to the rest of the modules. One ormore of the wires carry either raw or processed complex baseband datafrom each antenna module and distribute the data to other modules or aprocessor mounted inside the satellite housing to be used in the packetdecoding process. In an alternate embodiment, the communication betweenmodules is done via wireless communication instead of wiredcommunication. In an embodiment, the antennas are arranged on alternatemodules such that when the modules are folded, the antennas fold morecompactly by not overlapping with adjacent module antennas 6. FIG. 7illustrates more details of the electrical and mechanical connectionsbetween the antenna module circuit boards. One or more tape springs 7made out of steel or a composite material is attached along the edges ofthe antenna module circuit boards and exerts torque on adjacent antennamodules to unfold the antenna modules from the folded configuration whenthe antenna modules are not held inside the satellite housing. One ormore flexible PCBs 8 are used to electrically connect adjacent antennamodule circuit boards. Since the antenna array operates in a zerogravity environment, only a small torque is necessary to expand thefolded antenna modules out into a straight array.

The top and bottom view of an embodiment of a module used to construct alinear antenna array is shown in FIG. 8 , where each module ismanufactured from circuit board material and is mounted with a solarcell 9, one or more antenna elements 10, and RF, analog and digitalbeamforming circuitry 11. In an embodiment, to increase the compactnessof the folded antenna modules, openings in the circuit board consistingof slots or holes 12 are integrated into the module circuit boardmaterial which allows for the beamforming and other electroniccomponents from adjacent modules to fit into the slots or holes when themodules are folded. In an alternate embodiment, the solar cells can bemounted separately on the satellite housing, however mounting on theantenna module itself can provide additional volume efficiency. Themodule circuitry and solar cell is assembled on a glass reinforced epoxylaminate material or it can also be assembled on Teflon or othermaterials that allow for mounting of electronic components.

For better visualization, a side view of a satellite integrating linearantenna arrays is shown in FIG. 9 . The figure shows one of the spokes.The second spoke in the illustrated embodiment is perpendicular to thefirst spoke and is not shown in the figure. The spoke antenna elementspoint towards the earth as the satellite orbits. A GPS receiver 13 isused by the satellite to estimate its position. Magnetic sensors and astar tracker 14 are used to estimate the satellite attitude (roll, pitchand yaw). Magnetorquers 15 and reaction wheels 16 are mounted inside thesatellite housing and are used to control the satellite attitude.Batteries 17 contained within the satellite housing are used to providepower to the satellite electronics when the satellite is orbiting in theeclipse portion of the orbit. A separate bidirectional radio link 18 isused to communicate with one or more ground stations on earth. Thisradio link is used to send the collected endpoint packet data back downto earth and receive commands or firmware updates from the groundstations. The antenna spokes can be designed to be either one way (earthto satellite) or bidirectional. In the bidirectional case, the antennaspokes can be dual purposed to send data to either endpoints or to senddata back to a ground station using the same frequency band as theendpoint to satellite band. This would be done by time multiplexing thecommunication channel when the spoke antennas are single band antennas(this is called Time Division Duplexing). In an alternate embodiment,the antenna spokes are designed to be dual band, in this case, theantenna spokes can transmit on one frequency band and receive on asecond frequency band simultaneously (this is called Frequency DivisionDuplexing). FIG. 10 illustrates a side view of a satellite that has 4antenna spokes. Two of the antenna spokes that are perpendicular tospokes 1 and 3 are not shown. Spoke 1 and spoke 3 in the figure are at a90 degree relative yaw angle to each other, although not depicted in thefigure. To increase the compactness of the stowed antenna spokes in thefour antenna spoke case, in the embodiment the antenna spokes are placedin different z positions as shown in the figure.

FIG. 11 illustrates the side view of a satellite with the antenna spokes19 stowed inside the satellite. For clarity, only one of the spokeswhich has two branches is shown in the figure. When the antenna modulesare stowed away inside the satellite, they are held in place by either aburn wire 20 or mechanical door with a solenoid to release the door.Alternate embodiments can have other release mechanisms such as magneticlatches. Once the burn wire is burned or the mechanical door is opened,the antenna modules expand out and form two or more antenna spokes. FIG.12 shows a top view of the stowed antenna arrays for a two spokeconfiguration with two branches per spoke. The arrows show the directionin which the spokes expand out. The figure illustrates the spokebranches 21,22 where each branch has half the antenna elements that afull spoke has. This makes it simpler to stow away in a small volume.All antenna spokes and branches are electrically connected either toeach other or to a central processor to allow for the necessary signalprocessing of the down converted received signals, decoding the receivedpackets and sending the packets down to a earth based ground station.

The block diagram of an embodiment of the antenna module receiveelectronics is illustrated in FIG. 13A. The circuit is used todownconvert the RF signal to baseband and process the downconvertedreceived signal. Each antenna on the module feeds into a band passfilter 23 followed by a low noise amplifier (LNA) 24. An additional bandpass filter 25 can optionally follow the LNA to further reduce out ofband noise. An RF mixer 26 down converts the incoming signal to a lowerintermediate frequency (IF). The mixer is followed by an amplifier 27and an anti aliasing filter 28. The down converted signal is then fedinto an Analog to Digital converter (ADC) 29. The digitized signal isfed into a digital processor 30. The processor can be a microprocessor,a field programmable gate array or a custom digital ASIC. The processorreceives baseband signals from antenna modules in the array and performscomputations on the signals as described in paragraph [0063]. In analternate embodiment, the signal processing can be done on a processorthat is not located on the antenna array module but is located insidethe satellite main housing on a separate PCB. In an embodiment, thepacket decoding is performed locally on the satellite. In an alternateembodiment, the raw or partially processed down converted and digitizedcomplex baseband signals from each antenna can be sent down to a groundstation directly. When the satellite sends the complex baseband signalsdirectly to the ground station, the packet decoding process would beperformed at a computer or server located on earth. Sending the receivedcomplex baseband signals directly down to a ground station will howeverrequire higher satellite to ground station communication bandwidth.

In an embodiment, antenna modules are designed to provide bidirectionalcommunication with endpoints on the ground by integrating transmit radioelectronics into the modules. FIG. 13B illustrates the transmitelectronics circuitry, which includes a Digital to Analog converter 31(DAC) which receives the digitized, discrete time complex basebandinformation that is to be modulated onto the carrier and converts itinto an analog continuous time signal. The complex baseband signal canoptionally be injected into a lowpass filter 32 to filter out anyunwanted out of band signals and then the signal is amplified 33 andquadrature mixed 34 with the local oscillator signal. The signal is thenfurther amplified 35, and optionally filtered 36 to reduce any out ofband harmonics and the signal is then sent to the antenna. The receiveand transmit electronics can share the same antenna by time divisionduplexing the channel or by using a dual band antenna which allows forfrequency division duplexing. In an alternate embodiment, separatetransmit and receive antennas are mounted on each antenna module toavoid the need to share antennas between the transmit and receivecircuits. In the transmit direction, the gain and phase of the complexbaseband signal are selected to allow for pointing one or more transmitbeams in the direction of one or more endpoints. Multiple beams whereeach beam contains a different packet transmission can be createdsimultaneously with the correct choice of gains and phases both in thetransmit and in the receive direction. The signal processing performedon the received signals is described in the next section.

Each antenna array spoke is programmed to receive radio energy fromseveral focused zones that can have a varying degrees of beam overlap.For an N antenna linear array, there are approximately N/2 beams thathave small spatial overlaps in their radio receive beams over the spanof elevation angles from −45 degrees to 45 degrees. Although any numberof M beams can be formed which could have varying degrees of spatialoverlap among the beams. Higher beam overlap allows for betterpositioning accuracy of endpoint radio transmissions. Furthermore, sincesatellites travel at around 7.8 km/s in Low Earth Orbit, the beamoverlap also provides redundancy if an endpoint transmission is longenough to cross from one beam zone into an adjacent beam zone. FIG. 14illustrates the computations necessary to create M focused receive beams37 for a linear antenna array. The received baseband signals at each ofthe N antennas is denoted by x₁ through x_(N). These signals aremultiplied by a beamformer matrix, denoted by H. To create a beam, thebeamformer matrix phase shifts the received signals at antenna krelative to k—1 by a constant phase shift that depends on the spacingbetween the antennas and the elevation angle of the beam to be formed.The phase shifted signals from each antenna are then accumulatedtogether. The phase shift is chosen to add the radio energy at eachantenna in phase to maximize the signal strength for a specific beamdirection. The phase shift is computed by calculating the phasedifference in the radio arrival signal at each antenna for a specificbeam elevation angle along the direction of the antenna array. Thesephase shift values are then used by the beamformer matrix in the signalprocessing to align all the received signal phases by multiplying theincoming baseband signals by the complex conjugate of the complexexponents representing the predicted arrival radio wave phase shifts foreach beam elevation angle. When antenna spokes are broken into twobranches that are offset in space, the phase shift computation isadjusted to take into account the offset between the branches. Eachincoming baseband signal can also be multiplied by a gain factor totrade off a wider width of the main beam lobe for a smaller amplitude ofthe side lobes of the beams. To create M beams using an N antenna lineararray requires a matrix, H of size M×N which multiplies the incomingbaseband signals by the complex exponents (and possibly gains fortapering) to create the necessary phase shifts to align the receivesignals and create the beams. The phase shifts used in the receivedirection to form beams at specific elevation angles can also be used inthe transmit direction to form transmit beams along the same elevationangles. In an alternate embodiment, the beamformer matrix, H is chosensuch that the beams generated sweep the ground to counter the motion ofthe satellite and also adjusted to counter any changes in the satelliteattitude. In this case, each beam would be focused on a specific zone onearth and the beam coverage zone would not move with the satellitemotion. The beamformer matrix, H would be composed of time varyingcomplex exponents in this case.

For clarity, the orbital frame of reference is used for discussion ofgeometric concepts as shown in FIG. 15 . The azimuth angle is defined asthe angle of propagation of the radio wave relative to the direction ofthe orbital plane. The elevation angle is defined as the angle ofpropagation of the radio wave relative to the −Z axis of the orbitalframe of reference. When observing the beam patterns from earth, thebeam contours of maximal beam energy are parabolic in shape since thephase difference of the radio waves arriving at consecutive antennas area function of both the azimuth and elevation angles of the receivedradio waves in the spoke frame of reference. The phase difference of theradio wave carrier for consecutive antennas spaced half a wavelengthapart along a linear antenna array is computed as:

phase difference=π cos(azimuth_s)sin(elevation)  Equation 1

where azimuth_s is the azimuth angle in the spoke frame of reference(azimuth_s=0° is a radio wave arriving along the length of the spoke).FIG. 16 illustrates several beam contours for 9 beams formed by eachlinear antenna spoke for a two spoke system with perpendicular spokes.These contours would be observed on flat ground and the contours werecreated assuming a satellite altitude of 600 km. Ox and Oy denotes thephase difference of the arrival radio wave between consecutive antennasfor the x and y spoke respectively. The horizontal contours in thefigure are formed by the spoke that is pointing in the Y direction andthe vertical contours are formed by the spoke that is pointing in the Xdirection. In the orbital frame of reference, azimuth_x is defined asthe azimuth of the x spoke and azimuth_y is defined as the azimuth ofthe y spoke. When the spokes are perpendicular, azimuth_x=azimuth_y+90°.The phase differences among consecutive antennas for the two spokes ispre-computed for each of the formed receive beams. For the two spokeconfiguration, we get two equations and two unknowns when an endpointsymbol transmission is received by a beam from each spoke. The equationsare:

phase difference (y spoke)=π cos(azimuth_sy)sin(elevation)  Equation 2

phase difference (x spoke)=π cos(azimuth_sx)sin(elevation)  Equation 3

where azimuth_sy is the azimuth of the radio wave in the y spoke frameof reference and azimuth_sx is the azimuth of the radio wave in the xspoke frame of reference. Assuming that the pitch and roll angles of thesatellite is zero and converting this back into the orbital frame ofreference, the following equations are obtained:

azimuth_sy+satellite yaw angle=azimuth  Equation 4

azimuth_sx=azimuth_sy+ϕ  Equation 5

where ϕ is the orientation of the x spoke relative to the y spoke and is90 degrees when the spokes are perpendicular. The satellite yaw angle isdefined as the azimuth angle of the Y spoke relative to the orbitalplane. The known variables are the phase differences that generated thebeams from the two spokes. The unknowns are the azimuth and elevationangles of the radio wave corresponding to a symbol transmission from thecorresponding endpoint. From the above equations, the azimuth andelevation angles of the radio wave in the orbital frame of reference canbe computed. These angles define the endpoint position on the groundsince the satellite position and attitude relative to the earth is knownby using the on board GPS radio, magnetic sensors and sun sensor as wellas the attitude estimation method described later in the disclosure. Nonzero pitch and roll angles can be integrated into the above equationswith the proper rotation matrices. For each symbol received, the azimuthand elevation angles of the corresponding radio wave is computed asdescribed above and a position coordinate is assigned to the symbol.

For illustrative purposes, the beam contours are assumed to be straightalong the x and y axis. This simplification for illustrative purposes isshown in FIG. 17 for beam contours generated by the X spoke and FIG. 18for beam contours generated by the Y spoke. When an antenna spoke isrectangular and has more than one antenna along the narrow dimension,the beam contours will look similar except that the beam width can becontrolled in both the x and y dimensions. For simplicity thisdisclosure will focus on the case where perpendicular linear antennaarrays are used. When non linear, oblong shaped antenna arrays are used,the created beams are two dimensional instead of one dimensional. Thesame principals apply in solving for the position of an endpointtransmission in this case.

In the simplified case where the beam contours are approximated to bestraight lines, FIG. 19 illustrates the superimposed beam contours fortwo linear antenna arrays that are perpendicular to each other, creatingan array of x column beams and y column beams. When signals arrive atthe satellite at the x and the y linear antenna array spokes, theposition of the source of the radio wave can be estimated by convertingthe phase differences observed along the antenna spokes into the angleand elevation angles of the propagated radio wave and then into aposition on the earth. This can be visualized using the 2D matrix shownin the figure, where an endpoint transmits a symbol 38 from position row4 and column 2. The row and column position would translate to aposition on earth after adjusting for the non straight line beamcontours as described in paragraph [0064].

In radio communications, orthogonal modulation is used to improve theradio sensitivity for a target communication rate by spreading theavailable energy over as much bandwidth as is practical. The drawback oforthogonal modulation is that it suffers from low spectral efficiency.The combination of multi antenna spoke beamforming with orthogonalmodulation lends itself to significant performance improvements oversingle antenna radios that use orthogonal modulation by improving thespectral efficiency of the system. An example of orthogonal modulationis M-ARY Frequency Shift Keying (FSK) modulation. The FFT of an M-ARYFSK symbol is shown in FIG. 20 . Log₂(M) bits are mapped to one of Morthogonal frequency tones and one of the possible tones is sent outover the communication channel to encode the bits. FIG. 20 illustratesthe case when M=256, where 8 bits are encoded to a specific tonefrequency. The bits ‘01001110’=78 are encoded by the tone frequency inthe example. At the receiver, each received tone is then demodulated andtranslated back to the correct bits. In a shared wireless network, iftwo orthogonally modulated symbols that are sent from two differentendpoints overlap in time, the receiver can be confused as to whichsymbol corresponds to which transmitter. FIG. 21 depicts a spectrogramof two symbols from two different endpoints which overlap in time butnot in frequency. A symbol that overlaps in time with one or more otherorthogonal modulated symbols can only be guaranteed to be decodedcorrectly if the symbol to be decoded does not overlap with othersymbols over the range of orthogonal dimensions (for M-ARY FSK the rangeof orthogonal dimensions is the 2^(M) frequencies). The spectralefficiency of M-ARY orthogonal modulation using a single antennareceiver is approximately Log₂(M)/M bits/sec/Hz. With multi spokebeamforming, to improve the spectral efficiency, symbols from differentendpoints that overlap in time are assigned positions and can bedifferentiated based on each symbol position. This is illustrated inFIG. 22 which shows a first symbol 39 from a first endpoint picked up byrow beam 4 and column beam 3, and a second symbol 40 from a secondendpoint picked up by row beam 12 and column beam 3. If the two symbolsoverlap in time but not frequency, then the symbols can bedifferentiated and decoded individually since they are detected byunique pairs of row and column beams. To decode the two symbolssuccessfully with a single antenna receiver, the symbols would need tonot overlap in time or not overlap over the range of the orthogonalfrequencies.

FIG. 23 illustrates a case where a first endpoint transmits a symbol 41that is picked up by row beam 4 and column beam 3. A second endpointtransmits a symbol 42 that is picked up by row beam 12 and column beam3. A third endpoint transmits a symbol 43 that is picked up by row beam4 and column beam 13. If the second and third endpoint transmit theirsymbol at the same time as the first endpoint, and furthermore, if thesecond and third endpoint also transmit their symbol on the samefrequency as each other (but different than the first endpoint to avoidsymbol collision) there can be ambiguity when decoding the firstendpoint's symbol. The decoder can't tell if the overlapping symbolsfrom the second and third endpoint were actually one symbol that waspicked up by the intersecting row and column beams. This case however isless likely since it requires symbol overlaps in both time andfrequency. Ignoring this case, the spectral efficiency of a two spokelinear antenna receiver that uses M-ARY FSK modulation and N nonoverlapping beams per spoke has an upper bound of N*Log₂(M) bits/sec/Hz,an improvement of N*M over a single antenna receiver that uses M-ARY FSKmodulation. As a practical matter, satellite radio communications linkshave a limited elevation angle in which they work reliably due toincreased endpoint to satellite ranges at larger elevation angles andlower antenna gains at higher elevation angles. For this analysis it isassumed that the elevation angle is limited to a maximum of 45 degrees.In this case, a 128 antenna element linear array can create around 64non overlapping beams on the ground that covers a 45 degree elevationangle range. Including the cases where there are time and frequencyoverlaps of symbols as discussed earlier, a two spoke linear antennaarray system with 128 antennas per spoke and 64 non overlapping beamsusing 64-ARY FSK modulation has been simulated to have approximately700× better spectral efficiency compared to a single antenna receiverthat uses 64-ARY FSK modulation. For the same amount of bandwidth, thistranslates to a 700× improvement in network capacity. The same twoantenna spoke system using 64-ARY FSK modulation is simulated to havearound a 150× improvement in spectral efficiency vs. a single antennareceiver that uses 2-FSK modulation. A standard square antenna arraywith the same volume as a 128 element per spoke, two spoke linear arraywould have an array size of around 16×16 antenna elements and generate8×8=64 non overlapping beams on the ground over a 45 degree elevationrange. A two spoke linear antenna array with 128 antenna elements perspoke, receiving 64-ARY FSK signals would have approximately700/64=10.9× improvement in network capacity over the 16×16 squareantenna array that receives 64-ARY FSK modulated signals andapproximately 150/64=2.3× improvement in network capacity over a 16×16square antenna array that receives 2-FSK modulated signals. Anotheradvantage of using a plurality of spoke antenna arrays vs. squareantenna arrays is that the positions of endpoints on the ground can beestimated with higher accuracy for the same antenna volume. The positionaccuracy along the x or y dimension is inversely proportional to thelength of the antenna array along each of the dimensions. Two linearantenna arrays with 128 elements along each of the x and y dimensionswould be able to estimate an endpoint's position approximately 8× moreprecisely than a 16×16 element square antenna array (assuming the samespacing between antennas for the linear and square array).

Another advantage of using orthogonal modulation is an improvement inenergy efficiency. A 64-ARY FSK radio will need approximately 2× (3 dBin Decibel scale) less energy to send the same size packet compared to a2-ARY FSK radio over an Additive White Gaussian Noise (AWGN) channel(for 10% probability of symbol error). In summary, the multi spokebeamforming receiver provides significant improvements in both networkcapacity and energy efficiency compared to single antenna receivers. Themulti spoke architecture allows for a small volume antenna array that iseasily stowable in a small satellite and still provides good networkcapacity and spectral efficiency.

The multi spoke symbol decoding approach is not only applicable to M-ARYFSK modulation but also to any other orthogonal modulation scheme. FIG.24 shows the flowchart for decoding any packet that uses orthogonalmodulation. First M spatial beams are created for each antenna spoke 44,then for each beam created by each spoke, preamble detection circuitry45 searches for a sequence of preamble symbols along both spokes and allbeams. If a preamble sequence is detected simultaneously by two spokes,the preamble sequence is assigned a position 46. The system then looksfor follow on data symbol transmissions that are assigned the sameposition as the preamble transmission 47. Finally consecutive symbolsthat have similar positions as the preamble symbol sequence are groupedtogether and the packet containing these symbols is decoded 48.

The orthogonal signal decoders for different orthogonal modulations isdescribed in more detail in the following paragraphs. FIG. 25 shows thereception of an M-ARY FSK signal 49 where one of M orthogonal frequencytones are selected at the transmitter to encode a bit sequence. At thereceiver, for each beam of each antenna spoke, the signal is fed into anFFT 50. In an embodiment, the sample rate of the incoming signal intothe FFT is set to the bandwidth of the communication channel and thenumber of samples per FFT computation is set to the symbol durationmultiplied by the sample rate. For each antenna spoke beam, a preambledetector 51 searches over time and frequency for the preamble symbolsequence. When the preamble detector detects a valid preamble, thecircuit has obtained frequency and time synchronization with theincoming data packet. The preamble detection circuit outputs from allantenna spokes and beams is fed into a processor 52 which checks to seeif there are valid preamble sequences that appear at the same time andfrequency on receive beams of two different spokes. Once the processordetects a valid preamble sequence arriving on two different spokes atthe same time, the decoder is now time, frequency and spatiallysynchronized. The figure shows an example where spoke 1 beam m and spoke2 beam n both detect the preamble simultaneously. The decoder 53 thendecodes the data symbols arriving at the proper time, frequency andspace (intersection of the two beam contours on earth where the preamblewas detected). FIG. 25 shows the case where the data symbols associatedwith a preamble sequence arrives from the same row and column beams thatthe preamble symbol sequence arrived from. It is important to notehowever that the row and column beams that receives the preamble symbolsequence is not necessarily the same row and column beams that receivesthe associated data symbols. This is only true if over the duration ofthe packet transmission, the satellite motion and variation of satelliteattitude is small enough to not change the beams which receive the datasymbols compared to the beams that received the preamble symbolsequence. In the embodiment where the beam weights are time varying andselected to counter the motion of the earth and to adjust for thesatellite attitude, then the beams will track a fixed contour on earthand the same set of row and column beams that receive a preamblesequence will also receive the corresponding data symbols of a packet.During the decoding process, if a data symbol frequency does not matchup among the two spokes or if there is more than one frequency thatmatches up among the two spokes, then the data symbol is declared anerasure. The packet can still be decoded by using a proper errorcorrecting code that can correct a certain number of symbol errorsand/or erasures.

Another orthogonal signal that can be used with the multi spoke antennaarray receiver is the Chirp Spread Spectrum signal. FIG. 26 shows achirp spread spectrum modulated signal 54 that modulates bits based on acyclical time shift of a base chirp signal (a chirp with 0 time delay).At the receiver, for each beam of each spoke the chirp signal isconvolved by the base chirp signal. After convolution, when the receivedsymbols line up in time with the base chirp, the resultant signal issimply an M-ARY FSK modulated signal. The convolved signal is then fedinto an FFT block 55 and the remaining part of the decoding process isidentical to the M-ARY FSK decoding process.

The above examples demonstrated orthogonal signaling over the frequencydimension (M-ARY FSK, Chirp Spread Spectrum). It is also possible toachieve orthogonal signaling over the time dimension, code dimension ora combination of frequency, time and code dimensions. To achieveorthogonality over the time and/or the code dimensions, Direct SequenceSpread Spectrum (DSSS) signals are typically used. As a briefbackground, to achieve orthogonality over the code dimension, M DSSSsignals are generated. Each symbol is orthogonal to each other and eachsymbol encodes Log₂(M) bits as shown in FIG. 27A. To achieveorthogonality over the time dimension, a DSSS signal with good selforthogonal properties is chosen, such that time shifts of the same codesequence are orthogonal to other time shifts for multiples of the chipperiod T as shown in FIG. 27B. Sets of DSSS signals that achieveorthogonality over both the time and code dimensions can be chosen aswell. To achieve orthogonality over the frequency and time dimensions, aDSSS signal with good self orthogonal properties can modulate an M-ARYFSK signal. To achieve orthogonality over the frequency, time and codedomains, a set of K orthogonal DSSS signals are chosen, where each DSSSsignal also has good self orthogonal properties. Each DSSS signalmodulates an M-ARY FSK signal. To encode Log₂(M*K*T) bits per symbol,one of M of the FSK tones is selected, modulated by one of the Korthogonal DSSS signals and then time shifted by one of T time shifts.As more orthogonal dimensions are added, the decoder computationalcomplexity increases.

A decoder that can decode across orthogonal frequency and timedimensions is shown in FIG. 28 . In the Figure, a DSSS signal with goodself orthogonal properties modulates an M-ARY FSK signal. At thereceiver, for each beam of each spoke, the received signal 57 isconvolved with the DSSS signal matched filter. When the received symbollines up in time with the matched filter, we are left with an M-ARY FSKsignal. The signal is injected into an FFT block 58 and the remainder ofthe decoding process is the same as an M-ARY FSK decoder, except thatbits can also be encoded in time shifts of the symbol.

The above examples demonstrated orthogonal signaling over the frequencydomain (M-ARY FSK, Chirp Spread Spectrum) and orthogonal signaling overthe time and frequency dimensions (DSSS modulated M-ARY FSK signal withT possible time shifts of the data symbols). It is also possible togenerate orthogonal signals over the code dimension, over the code andtime dimensions, and over the code, time and frequency dimensions. Amore computationally complex decoder that can decode symbols over allthree dimensions is shown in FIG. 29 . In the Figure, a DSSS signal ispicked from an alphabet of K orthogonal codes, where each code has goodself orthogonal properties and modulates an M-ARY FSK signal. A timeshift T is also added to each transmission to encode bits along the timedimension. At the receiver, for each beam and each spoke, the receivedsignal 59 is convolved with a bank of matched filters 60, where eachmatched filter is one of the K DSSS signals. When the received symbollines up in time with one of the matched filters, we are left with anM-ARY FSK signal. Each of the matched filter outputs is injected into anFFT block 61 and the remainder of the decoding process is the same as anM-ARY FSK decoder, except that additional bits can also be encoded intime shifts of the symbol and in the code that was chosen for eachsymbol. The preamble detector now searches over time, frequency and thecode dimensions during the preamble search process.

FIG. 30A through FIG. 30C illustrates two endpoints transmitting symbolsalong different orthogonal dimensions. For orthogonal signaling over thefrequency dimension as shown in FIG. 30A, the multi spoke arrayprocessing allows for resolving ambiguity that occurs when symbols don'ttransmit using the same frequency but do transmit over the same symbolfrequency range used to encode the bits. For orthogonal signaling overthe frequency and time dimensions as shown in FIG. 30B, the multi spokearray processing allows for resolving ambiguity that occurs when symbolsfrom different endpoints don't collide in time and frequency but dotransmit over the same time and frequency range that is used to encodesthe bits. For orthogonal signaling over the time, frequency and codedimensions as shown in FIG. 30C, the multi spoke array processing allowsfor resolving ambiguity that occurs when symbols from differentendpoints do not collide in time, frequency and code space but dotransmit over the same time, frequency and code range that is used toencode bits. In general, the improved spectral efficiency/capacityimprovement is independent of the type of orthogonal modulation used, itonly depends on the number of symbols used in the alphabet to encodebits and the number of antennas used in the antenna array spokes.

As the satellite moves towards an endpoint that is transmitting apacket, the transmitter's observed carrier frequency will increase. Theobserved carrier frequency will decrease when the satellite is movingaway from the endpoint. This change in observed frequency is due to theDoppler shift which is equal to v*f/c, where v is the relative velocityof the satellite to the endpoint, f is the carrier frequency and c isthe speed of light. This Doppler shift is shown in FIG. 31 for asatellite that varies in position from −600 km to 600 km relative to theposition of the endpoint along the direction of travel. For a 2.4 GHzcarrier frequency, the Doppler shift varies from around −35 KHz to 35KHz for a satellite altitude of 600 km and velocity of 7.6 km/s. If thefrequency shift was constant, it would not be a problem since thereceiver would be able to lock onto the carrier frequency when searchingfor the preamble. The challenge becomes dealing with the change inDoppler shift over multiple data symbols which can cause the receiver tolose frequency synchronization and erroneously decode symbols. This isclear to see in the M-ARY FSK case as an example, where assuming eachsymbol is spaced by 125 Hz, a small change in Doppler shift of around125 Hz can cause the bits to be decoded incorrectly. The change inDoppler frequency for a carrier frequency of 2.4 GHz and over a typicalpreamble duration of 50 mS is shown in FIG. 32 . As shown in the figure,the worst case frequency change over the duration of the preamble isaround 30 Hz. The preamble detection circuit would still be able to lockonto the preamble even with this shift and would be impacted with only asmall degradation in performance (around 0.5 dB reduction in preambledetection sensitivity for 8 mS long symbols). The process of Dopplercorrection for an orthogonal or non orthogonal signal decoder is shownin FIG. 33 which works for all orthogonally and non orthogonallymodulated signals including but not limited to M-ARY FSK, Chirp SpreadSpectrum, Direct Sequence Spread Spectrum, BPSK and QPSK signals.Multiple signal demodulators 62 processes the incoming signals from allof beams and every spoke. A preamble detector 63 operates along eachbeam and searches for a sequence of preamble symbols. When preambledetections occur simultaneously on a row and column beam, the positionof the preamble transmission is estimated 64. The figure shows anexample where spoke 1 beam m and spoke 2 beam n both detect the preamblesimultaneously Using the preamble position estimate, the change inDoppler frequency shift for the remainder of the packet data symbols isestimated 65 by looking up the deterministic Doppler frequency variationover time curve 66 for the estimated endpoint position. Instead of alookup table the Doppler frequency variation over time can be computedanalytically as a function of the endpoint position relative to thesatellite position and the known satellite velocity. Each data symbolthat is received from the correct spatial position after the preamblesequence is then frequency adjusted 67 based on the estimated Dopplercorrection factor that is computed from the Doppler frequency variationover time curve. The frequency adjusted symbols are then sent to thepacket decoder 68 which translates the data symbols into bits, andoptionally applies bit de-interleaving and error correction to the bits.

Typically, satellites will use star trackers and magnetic sensors toestimate the satellites attitude (pitch, roll and yaw). Satellites canuse a radionavigation system such as the Global Positioning System (GPS)to compute its three dimensional position coordinates. However theposition and attitude estimates are not always very precise and it isbeneficial to be able to estimate the satellite position and attitudeusing additional means. To do so, the proposed system relies on aplurality of radio transmitters on the ground with known positions. Theground based transmitter position can be either static or dynamic asshown in FIG. 34 . These ground based transmitter positions can beestimated either in real time by using an on board GPS receiver orduring the transmitter installation assuming that it is a statictransmitter. The transmitters are either static transmitters 69 ormobile transmitters. Mobile transmitters can include standard smartphones 70 that have GPS for estimating their position and the ability tocommunicate with the satellite. The transmitters can also be endpointson the ground that have integrated GPS receivers and can send their GPSposition to the satellite 71. Any combination of radio transmitters witha known location can be used for satellite position and attitudeestimation. These transmitters send a periodic message to the satellite,where the message contains the transmitter's position. To estimate thesatellite position and attitude, six or more transmitters that arespread out far enough on the ground transmit their known positions atapproximately the same time to the satellite. If the satellite positionis already known using a radionavigation system such as GPS 72 forexample, then only three or more transmitters on the ground are neededto estimate the three attitude variables. The ground based transmitterscan be time synchronized using GPS time synchronization or other meanssuch as network time protocol for example. To allow for more precisesatellite position or attitude estimation, the ground based transmittersshould be spread out in both the latitude and the longitude directionsby approximately the antenna array beam width spacing or more. Thesatellite antenna arrays receive the position information from theground based transmitters. The satellite combines the positioninformation received from the ground based transmitters together withthe angle of arrival estimates of each transmitter's transmission. Theequations can be solved for the unknown position and attitude variables(elevation, azimuth, range, pitch, roll and yaw). With more than sixtransmitters on the ground spaced far enough apart such that eachtransmitter is at least a beam width apart from other transmitters, theset of equations is over-determined, and a least squares estimate can becomputed to improve the accuracy of the satellite attitude estimate. Ifthe transmissions from the ground based transmitters do not occur at thesame time, a Kalman filter on the satellite integrates the position datafrom the ground transmitters along with satellite inertial measurementsto compute an estimate of the satellite position and attitude. Theposition and attitude estimates can also be continuously updated by theKalman filter in between transmissions since transmissions might notoccur continuously to reduce the uplink bandwidth required. The positionand attitude estimation computations can be done locally on thesatellite or remotely on a server.

Satellite based IoT networks work well for rural and suburbanenvironments but face challenges in urban environments with radio waveblockage by tall buildings and higher levels of radio interference. Forurban environments it is beneficial to complement the satellite networkwith a terrestrial network to offload the satellite network and providemore reliable coverage. The multi spoke beam forming technologydiscussed for satellites can also be applied to terrestrial networkswith a small architectural change. Instead of having multiple oblongshaped antenna arrays co-located like in the satellite case, in theterrestrial case two or more antenna arrays are installed ingeographically separate locations where each antenna array is mountedparallel to the ground and in an orientation that allows for creation ofradio beams parallel to the earth. A top view of this architecture isshown in FIG. 35 and FIG. 36 . Each antenna spoke 73 creates N receiveradio beams, for illustrative purposes each spoke in the figure includes4 antennas 74. When a preamble symbol sequence is sent from an endpoint75, it is received by spoke 1, beam m and spoke 2 beam n as shown inFIG. 36 . For each follow on data symbol that is transmitted by theendpoint that belongs to the same packet, the same beams from each spokeshould pick up the symbols (assuming that the endpoint motion is fairlysmall during the packet transmission). Other endpoints that havedifferent positions will transmit symbols that are picked up bydifferent beams, and even when symbols overlap in time, they can bedifferentiated spatially, similar to the satellite case. In thesatellite case, when multiple data symbols arrive at the antenna arrays,the decoding can be done locally. In the terrestrial case, since theantenna arrays are spatially separated, the symbols need to betransmitted over wired or wireless means and processed either at aprocessor node 76 that is co located with one of the antenna spokes or ageographically separate location. The antenna spoke data can also berouted through the internet to the processing node. Similar to thesatellite case, the terrestrial antenna spoke positions and orientationscan be estimated using multiple transmitter nodes on the ground withknown positions that are spatially separated such that eachtransmitter's radio transmission is picked up by different receivebeams. If the yaw angles of the antenna arrays are known but thepositions of the arrays are not known, two transmitters with knownpositions would be needed to estimate the unknown antenna arraypositions. If the yaw angles of the antenna arrays are also not known,four transmitters would be needed for a two antenna array system. Unlikethe satellite case, in the terrestrial case, this calibration only needsto be done once since the terrestrial antenna arrays are static. In theterrestrial antenna array calibration case, a single transmitter canalso be used in multiple positions and the transmissions can be donesequentially and combined by the terrestrial antenna arrays for positionand attitude estimation.

The multi spoke decoding process can also be applied to oblong antennaarrays mounted on other platforms such as aircrafts. Additionally, thedecoding process can leverage multiple antenna beams, where each antennabeam is generated from a different platform. For example, one beam canbe generated from an antenna array that is mounted on a base station onthe ground and a second antenna array can be mounted on a satellite. Thepreamble symbol sequence and data symbol detections can occur at thevarious antenna arrays and the detections can be sent to a server orother location to aggregate the detections and apply the decodingmethods described in this disclosure.

There are advantages to having a single radio that can communicate overa broad range of networks, all the way from personal area networks (PAN)like Bluetooth Low Energy (BLE) to longer range Local area networks(LAN) like WiFi to longer range terrestrial low power wireless networks(LPWAN) and finally to satellite networks. In order to enable theseamless transition between networks, the endpoint radio first attemptsto establish communications with the lowest power network which istypically the PAN or LAN network. If communications cannot beestablished, the radio then attempts to communicate with the terrestrialLPWAN network. Finally, the endpoint radio sends its message to thesatellite network if no other network is available. This is shown inFIG. 37 .

The multi spoke beamforming architecture can also be applied in thetransmit direction to both send data to endpoints and also provideendpoints with the ability to locally compute their position as analternative to using a separate GPS receiver. The benefit of this isthat the same radio that is used by the endpoints for transmitting tothe satellite can be used by the endpoint to estimate its positionlocally. While the endpoint position is also estimated at the satellitewhen the satellite receives endpoint packet transmissions, there arecases where it is beneficial for the endpoint to compute its positionlocally without needing to send a packet to the satellite. An example isa geo-fencing application where an endpoint only needs to transmit apacket up to the satellite when it is outside of a certain geographicregion. In this case it is more energy efficient for the endpoint toonly transmit when it is confident that it is outside of the geofenceboundary. In order to implement this functionality, this process isillustrated in FIG. 38 . A beam is generated from one of the antennaspokes and swept along the direction that the spoke is pointing. In anembodiment the sweep angle is from an angle of −45 degrees to 45 degreesin the elevation direction. The number of beam positions along the sweepshould be enough so that every point on the ground will get strongcoverage at some point along the sweep. At each step of the beam, theantenna array sends a beacon packet which contains the time, thesatellite position, the beam position and optionally a terraincorrection factor. The terrain correction factor provides an estimate ofthe local terrain elevation profile so that this can be factored in whenestimating the endpoint position. To estimate the endpoint position, theendpoint needs to receive information from at least two antenna spokes.Each antenna spoke independently sweeps the generated beam in space.Collisions between beams is avoided by time multiplexing the packettransmissions from each of the beams. The endpoint integrates thisinformation from multiple antenna spokes to estimate its position. Tosave power, in one embodiment, the endpoints are provided with ephemerisdata in the beacons which lets the endpoints know at what timessatellites will be above them and when to expect the next beams toarrive at their locations. This allows the endpoints to sleep as long aspossible before waking up their radios to listen for the next beacons toarrive. Ephemeris data can also be loaded into the endpoint by othermeans such as a nearby smartphone or cellular network.

When operating a radio in the unlicensed band, the radio needs tocontend with external interference that arises from multiple potentialsources. For example, when operating in the 2.4 GHz unlicensed band,other interference sources include WiFi radios, Bluetooth radios andmicrowave ovens. A satellite orbiting over the earth that is integratedwith the multi spoke antenna array architecture creates beams on theearth that are fairly narrow in width. The narrower the beam width, themore interference that the antenna array can spatially filter out,improving the performance of the satellite based gateway receiver. Thereare certain cases where an antenna beam might still contain significantinterference. For example, FIG. 39A illustrates the case where asatellite 77 is flying over the United States of America and a beamgenerated by the x spoke contains two urban areas 78. An urban areatypically contains significantly more sources of interference than ruralareas. It is thus beneficial to develop approaches that reduce theinterference that each antenna array beam picks up. One approach toreduce the received interference is to find the optimal yaw angle of thesatellite such that the interference picked up by the antenna arraybeams is minimized. FIG. 39B illustrates the case where the satelliteyaw angle is rotated by 45 degrees so that the antenna array beam onlypicks up one urban area instead of two urban areas, thus reducing theamount of interference picked up by the antenna array beam. To find theoptimal yaw angle, the following approaches are taken. The firstapproach is to measure the interference levels measured at each antennaarray beam as the satellite orbits the earth. When a second satelliteorbits along approximately the same orbital plane, the second satellitecan align itself to a different yaw angle relative to the firstsatellite. The second satellite then measures the interference level atapproximately the same position that the first satellite measured theinterference level. Interference measurements for each position along anorbital plane and each antenna spoke beam and each yaw angle is storedin memory and optionally can be sent down to the ground station and to aserver which aggregates all interference measurements from allsatellites in the network. Assuming that the interference levels staysrelatively constant over time, the system can learn over time what theoptimal yaw angle for each satellite is as it orbits above a certainlocation above earth. In an embodiment, the optimal yaw angles arecomputed on a server and sent back to the satellites using the groundstation to satellite wireless communication links. Another approach isto average out the interference by having each satellite continuouslyrotate in yaw angle as it orbits the earth. In an embodiment therotation period is chosen so that the rotation period is approximatelyequal to the packet duration.

Although the foregoing descriptions of certain preferred embodiments ofthe present invention have shown, described and pointed out somefundamental novel features of the invention, it will be understood thatvarious omissions, substitutions, and changes in the form of the detailof the apparatus as illustrated as well as the uses thereof, may be madeby those skilled in the art, without departing from the spirit of theinvention. Consequently, the scope of the present invention should notbe limited to the foregoing discussions.

What is claimed is:
 1. A satellite, comprising: a satellite housing; aplurality of foldable oblong shaped antenna arrays disposed inside ofthe satellite housing when the antenna arrays are in a foldedconfiguration, and extending outside of the satellite housing when theantenna arrays are in an unfolded configuration; and one or morestructures for deploying the antenna arrays from the foldedconfiguration inside of the satellite housing to the unfoldedconfiguration outside of the satellite housing; wherein the antennaarrays are constructed on a plurality of respective circuit boards, eachcircuit board is electrically connected to one or more antennas of theantenna array on the circuit board, each of the one or more antennasfeeds into a digital beamforming circuit on the circuit board, thecircuit board is electrically connected to an adjacent circuit board. 2.The satellite of claim 1 wherein each antenna of each antenna arraycomprises at least one solar cell on the respective circuit board. 3.The satellite of claim 1 wherein antennas of each antenna array do notoverlap with antennas of an adjacent antenna array when the antennaarrays are in the folded configuration.
 4. The satellite of claim 1wherein each circuit board includes openings, and a digital beamformingcircuit of an adjacent circuit board fits inside the openings of thecircuit board when the antenna arrays are in the folded configuration.5. The satellite of claim 1 wherein the one or more antennas feedinginto the digital beamforming circuit are patch antennas, helicalantennas, or monopole antennas.
 6. The satellite of claim 1 wherein theantenna arrays are electrically interconnected along edges of thecircuit boards.
 7. The satellite of claim 6 wherein one antenna arraydistributes a common radio frequency (RF) oscillator signal to otherantenna arrays.
 8. The satellite of claim 1 wherein the antenna arrayscommunicate with one another via a wired or wireless communication. 9.The satellite of claim 1 wherein the antenna arrays collectively form anantenna spoke.
 10. The satellite of claim 9 wherein the antenna spoke isconfigured one way or bidirectional.
 11. The satellite of claim 9wherein the antenna spoke is programmed to receive radio energy fromfocused zones having varying degrees of beam overlap.
 12. The satelliteof claim 1 wherein the antenna arrays are connected to each other or toa central processor to enable signal processing of down convertedreceived signals, decoding received packets, and sending the decodedpackets to a ground station.
 13. The satellite of claim 1 wherein theantenna arrays provide bidirectional communication with endpoints.
 14. Asystem, comprising: a plurality of foldable oblong shaped antenna arraysdisposed inside of a satellite housing when the antenna arrays are in afolded configuration, and extending outside of the satellite housingwhen the antenna arrays are in an unfolded configuration; and one ormore structures for deploying the antenna arrays from the foldedconfiguration inside of the satellite housing to the unfoldedconfiguration outside of the satellite housing; wherein the antennaarrays are constructed on a plurality of respective circuit boards, eachcircuit board is electrically connected to one or more antennas of theantenna array on the circuit board, each of the one or more antennasfeeds into a digital beamforming circuit on the circuit board, thecircuit board is electrically connected to an adjacent circuit board.15. The system of claim 14 wherein each antenna of each antenna arraycomprises at least one solar cell on the respective circuit board. 16.The system of claim 14 wherein antennas of each antenna array do notoverlap with antennas of an adjacent antenna array when the antennaarrays are in the folded configuration.
 17. The system of claim 14wherein each circuit board includes openings, and a digital beamformingcircuit of an adjacent circuit board fits inside the openings of thecircuit board when the antenna arrays are in the folded configuration.18. The system of claim 14 wherein the one or more antennas feeding intothe digital beamforming circuit are patch antennas, helical antennas, ormonopole antennas.
 19. The system of claim 14 wherein the antenna arraysare electrically interconnected along edges of the circuit boards.
 20. Amethod, comprising: providing a plurality of foldable oblong shapedantenna arrays that are disposed inside of a satellite housing when theantenna arrays are in a folded configuration, and extended outside ofthe satellite housing when the antenna arrays are in an unfoldedconfiguration; and providing one or more structures to deploy theantenna arrays from the folded configuration inside of the satellitehousing to the unfolded configuration outside of the satellite housing;wherein the antenna arrays are constructed on a plurality of respectivecircuit boards, each circuit board is electrically connected to one ormore antennas of the antenna array on the circuit board, each of the oneor more antennas feeds into a digital beamforming circuit on the circuitboard, the circuit board is electrically connected to an adjacentcircuit board.